Brightwell, Graham and Winkler, Peter (2002) Hard constraints and the Bethe Lattice: adventures at the interface of combinatorics and statistical physics. In: Proceedings of the International Congress of Mathematicians: Beijing 2002, August 20-28 (International Congress of Mathematician. Higher Education Press, pp. 605-624. ISBN 9787040086904
Full text not available from this repository.Abstract
Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for the study of phase transition. In this paper we survey recent work (concentrating on joint work of the authors) in which hard-constraint systems are modeled by the space $\hom(G,H)$ of homomorphisms from an infinite graph $G$ to a fixed finite constraint graph $H$. These spaces become sufficiently tractable when $G$ is a regular tree (often called a Cayley tree or Bethe lattice) to permit characterization of the constraint graphs $H$ which admit multiple invariant Gibbs measures. Applications to a physics problem (multiple critical points for symmetry-breaking) and a combinatorics problem (random coloring), as well as some new combinatorial notions, will be presented.
| Item Type: | Book Section |
|---|---|
| Official URL: | http://www.mathunion.org/activities/icm/previous/2... |
| Additional Information: | © 2002 The author |
| Divisions: | LSE |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 06 Feb 2012 16:36 |
| Last Modified: | 13 Sep 2024 15:37 |
| URI: | http://eprints.lse.ac.uk/id/eprint/10602 |
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